This invention relates generally to multistage turbocompressors and more particularly to a type thereof wherein the impellers of a plurality of rotary compressors are mounted on each of a plurality of rotating shafts, and all of the compressors are connected by gas conducting means to constitute a single multistage combination of the compressors in successive compression stages. An important feature of this multistage compressor of this invention is that an impeller of a preceding stage among the impellers on each shaft has an exit flow angle which is less than that of the impeller of the succeeding stage thereby to cause the specific (rotational) speed of each impeller to be within its optimal range.
In general, a gaseous fluid such as air or a gas possesses compressibility, and, therefore, when the gaseous fluid is compressed for the purpose of raising its pressure, its volume decreases according to Boyle's law (also known as Mariotte's law) as is well known. For a 4-stage compressor to suck in air and produce a discharge or delivery pressure of 7 kg.f/cm.sup.2 G, it is necessary that the pressure ratio (i.e., the ratio of the absolute discharge and suction pressures) of each stage be selected at a value of the order of 1.7, and the volumetric flow rate of the gaseous fluid sucked into a fan wheel or impeller is reduced approximately 60 percent upon reaching the entrance of the succeeding stage.
For the purpose of obtaining a discharge or delivery pressure of 7 kg.f/cm.sup.2 G with 3-stage compression, it is necessary to select a pressure ratio of approximately 2 for each stage. In this case, the volumetric flow rate at the entrance of the impeller of the succeeding stage is decreased to approximately 50 percent of that of the preceding stage. Thus, as the pressure ratio per stage increases, the rate of decrease of the volumetric flow rate of the gaseous fluid sucked into the impeller of a succeeding stage increases.
On one hand, in order for the impeller of each stage to exhibit high efficiency, it is required that the specific (rotational) speed N.sub.s expressed by the following equation be within an optimum range for each stage. EQU N.sub.s =N.multidot.Q.sup.1/2 /H.sub.ad.sup.3/4, (1)
where: N is the impeller rotation speed (r.p.m.); Q is the volumetric flow rate (m.sup.3 /min.) of each stage; and H.sub.ad is the adiabatic head (m.) of each stage. This specific speed N.sub.s is derived from the fluid mechanical law of similarity of turboblowers and compressors. It is a quantity having an important relation to the performance of the turbomachine and is an essential factor also in the selection of the type of the impellers.
Among the types of impellers, the common types are the centrifugal type, the diagonal-flow or "mixed-flow" type, and the axial-flow or propeller type. For each type, there is an optimum specific speed, and impellers of equal specific speed N.sub.s become geometrically similar impellers irrespective of their sizes and their rotational speeds. Furthermore, the optimum value of the specific speed N.sub.s has the characteristic of increasing with increasing width of the impeller blades in the centrifugal type and, further, with transformation into the diagonal-flow type.
Heretofore, in multistage turbocompressors, the impellers of the multiple stages have been of the axial-flow type, the centrifugal type, or a combination of the two types. For example, in one common type, centrifugal type impellers of two compressors of end-suction type are fixedly mounted respectively on opposite cantilever end portions of a single rotating shift. The two impellers are thus mounted at spaced-apart positions with their suction entrance sides facing away from each other. The shaft is driven by power transmitted to a driven gear fixedly mounted thereon at its middle part between the two impellers. One of the compressors is a first-stage compressor whose entrance is an end-suction port and its exit or discharge port is connected by way of a pipeline or flow passage to the entrance port of the other compressor, which is a second-stage compressor. Thus, the two compressors in combination constitute a two-stage compressor. The outer diameters of the first-stage and second-stage impellers are D.sub.a and D.sub.b, respectively.
In a multistage compressor of this character employing only centrifugal type impellers, it is necessary to make all impellers geometrically similar in order to cause the specific speed N.sub.s of each impeller to be of optimum value. For this purpose, since the suction volumetric flow rate Q decreases in the downstream stages, as mentioned hereinabove, it is necessary to reduce the size of the downstream stage impeller in accordance with the decrease of the flow rate Q. More specifically, it is necessary to reduce the outer diameter D.sub.b of the second-stage impeller in the above described example, for instance.
On one hand, since the adiabatic head H.sub.ad is proportional to the square of the outer circumferential velocity of an impeller, it is necessary to increase the rotational speed of the second-stage in inverse proportion to the impeller outer diameter, in order to make equal the adiabatic heads H.sub.ad and hence the pressure ratios of the stages. In order to realize this in actual practice, however, it is necessary to mount the impellers on separate, respectively independent rotating shafts, which will give rise to an increase in the number of machine parts and complication of the compressor construction.
Accordingly, it has been a practice heretofore to install two compressors on a single rotating shaft, whereby the rotational speeds of the impellers of the two compressors are made equal, and to make the shapes of these impellers substantially geometrically similar with the outer diameter D.sub.b of the second-stage impeller made smaller in proportion to .cuberoot.Q. The reason for this is that the relationships between the adiabatic head H.sub.ad and the impeller outer diameter D and the volumetric flow rate Q are as follows. ##EQU1##
More specifically, in the above described example of a two-stage compressor with impellers mounted on a single shaft, the following equation is used in its design. EQU D.sub.b /D.sub.a .apprxeq..cuberoot.Q.sub.b /Q.sub.a, (5)
where Q.sub.a and Q.sub.b are the suction volumetric flow rates of the impellers of the first and second stages, respectively. In the case of a pressure ratio of 2 as mentioned hereinbefore, the suction volumetric flow rate Q.sub.b of the second stage is 50 percent of that of the first stage. For this reason, the impeller outer diameter D.sub.b of the second stage, from Eq. (5), is .cuberoot.0.5, that is, 79 percent, of the impeller outer diameter D.sub.a of the first stage. Therefore, the adiabatic head of the second stage decreases to (0.79).sup.2, that is, 63 percent, of that of the first stage.
For this reason, in order to obtain a specific pressure rise required of the compressor as a multistage turbocompressor, it is necessary to increase further the rotational speed of the common shaft or to increase the number of stages. However, the former measure is not possible in the case where the outer circumferential velocity of the impeller of the first stage is the allowable limit for the material of the impeller, while the latter measure leads to not only high cost but ordinarily also to difficulties relating to construction.
Furthermore, even in the case where, fortunately, the required rotational speed of the shaft is within the limits set by the strength of the material of the first-stage impeller and the required fluid mechanical performance, since the centrifugal force acting on the second-stage impeller decreases in proportion to the square of the outer circumferential velocity, it becomes 63 percent of the centrifugal force of the first-stage impeller. This means that this centrifugal force of the second-stage is much lower than the allowable stress based on the strength of the impeller material, whereby the second-stage impeller has superfluous strength from the viewpoint of efficiency of material utilization, and the cost is unnecessarily high.